I only used a solenoid when I used my big compressor. You need something to cut the air off when the furnace is shut down or it would continue to blow air and siphon fuel along with it. I just left mine in when I got my vacuum pump because I was lazy, but really wouldn't need it because the pump switches on and off with the burner with no storage tank to keep supplying air so it quits just as soon as the pump stops.
I am no expert on capacitors, but mine has an Amrad R2000/37-156 on it.
Hope that helps.